The design of tooth restorations requires a deep dental knowledge. The challenge of computer aided tooth design lies in the computation of a functional correct morphology of the missing chewing surface. A solution must be robust and automated such that the user actually benefits from time saving and better results.
The article “Dental inlay and onlay construction by iterative Laplacian surface editing” by T. Steinbrecher et al. (Eurographics Symposium on Geometry Processing 2008; July 2-4, 2008 in Copenhagen, Denmark; Volume 27(2008), No. 5; p. 1441-1447) discloses that a model tooth may be adapted by using Laplacian surface editing to a patient's tooth. After adaptation, the part of the model tooth lying above the cavity will be joined with the cavity mesh to create the actual inlay reconstruction. The part of the model tooth lying above the healthy part of the tooth should be adapted to the remaining tooth surface. The model tooth is segmented into parts that lie “above cavity” or “on surface”.
From each vertex of the model tooth that is not yet clarified as “above cavity”, two rays are cast, one towards the centre of the tooth to be reconstructed, and one away from it. Thereby all rays by definition pass through the centre of the tooth to be reconstructed. Only the closest hit point is considered. The hit points are then classified according to their location as “above cavity”, “on surface”, or “undefined”.
The adaptation is an iterative process, alternating segmentation and deformation. For vertices classified as “on surface”, ray collisions with the tooth to be reconstructed are used again.
As the rays are cast, for each iteration, starting from a vertex of the model tooth also the segmentation has to be performed again. This is because by starting from a vertex of the model tooth, it is unknown where the location of a hit point on the tooth to be reconstructed will be. Even before the first deformation of the model tooth it needs to be segmented.
Desired deformation vectors may be weighted by deformation weights and further a global deformation weight linearly depending on the iteration step may be used as a scaling factor for all weights.
After the adaptation is completed, all vertices classified as “on surface” and not having a neighbor that is classified as “above cavity” will be removed and thus a mesh that covers the cavity remains wherein its boundary is aligned to the preparation margin.